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Unformatted text preview: MSIT 3000 Chapter 7: Randomness and Probability There are two main ideas we need to understand well before moving on to inference random chance Probability allows us to make the jump from simply describing a sample to drawing conclusions, or inferences, about the population. The purpose of this chapter is to see what the laws of probability tell us without going into the mathematics of probability theory. 87 MSIT 3000 Section 7.1: Random Phenomena and Probability Randomness and Probability Random behavior is unpredictable in the short run but has a regular and predictable pattern in the long run. Though used to predict a short term outcome, probability describes only what happens in the long run. We call a phenomenon random if individual outcomes are uncertain but there is nonetheless a regular distribution of outcomes in a large number of independent repetitions. The probability of any outcome of a random phenomenon is the proportion of times the outcome would occur in a very long series of independent repetitions. 88 For any random phenomenon, each attempt, or trial , generates an outcome . We use the more general term event to refer to outcomes or combinations of outcomes. Sample space is the collection of all possible outcomes . We denote the sample space S . The probability of an event is its long-run relative frequency. Empirical probability is based on repeatedly observing the events outcome. Independence means that the outcome of one trial doesnt influence or change the outcome of another. 89 Imagine rolling a fair 10-sided die and counting the number of times you roll a 2, 3, 7, or 8 (those values are a success and all other 6 possible values dont count). Roll this die 100 times, 100 more times, 200 more times, etc....
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